Derivative of SQRT(X + Sin^2 (3x) )

The original equation is as follows: SQRT(X + Sin^2 (3x) )... I tried to work it out and got the answer to be: 3(X+sin^2(3x)) ( X + sin(3x)) can someone verify if this is right or wrong for me please? Sorry I can't use code to type these problems. Thanks

so make repeated use of the chain rule. Step one is to wonder what the derivative of sqrt(y) is? then go on to work out [sqrt(y)]' * y', where of course the first derivative is with respect to y, and the second with respect to some x on which y depends.

then treat y' as a whole new problem, and forget what you've done thus far for the moment.

I'll start you up:

derivative =[1/2(sqrt(x+sin^2(3x))] * [x+sin^2(3x)]'

and now repeat, what is the next rule first? sum rule or chain rule? and after that? and after that again?